The total number of $6$ digited numbers greater than $400000$ that can be formed by using the digits $0,2,2,4,4,5$, is

The correct option is B $90$
$400000$ is a $6$-digit number and the number of digits to be used is also six. Also, the numbers have to be greater than $400000,$ so they can begin with either $4$ or $5.$

Case $1:$ When $4$ occupies the extreme left position.
Here we have to fill up the remaining $5$ places with the digits $0,2,2,4,5$ out of which $2$ appears twice.
This can be done in $\frac{5!}{2!}=60$ ways.

Case $2:$ When $5$ occupies the extreme left position.
Here we have to fill up the remaining $5$ places with the digits $0,2,2,4,4$ out of which $2$ and $4$ appear twice.
This can be done in $\frac{5!}{2!\cdot 2!}=30$ ways.

Hence, total number of required numbers is $60+30=90.$